
05380369
a
05380369
Horton, Matthew D.
Stark, H.M.
Terras, Audrey A.
Zeta functions of weighted graphs and covering graphs.
Exner, Pavel (ed.) et al., Analysis on graphs and its applications. Selected papers based on the Isaac Newton Institute for Mathematical Sciences programme, Cambridge, UK, January 8June 29, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 9780821844717/hbk). Proceedings of Symposia in Pure Mathematics 77, 2950 (2008).
2008
Providence, RI: American Mathematical Society (AMS)
EN
Zbl 1222.11109
http://www.math.ucsd.edu/~aterras/cambridge.pdf
Summary: We find a condition for weights on the edges of a graph which insures that the Ihara zeta function has a 3term determinant formula. Then we investigate the locations of poles of abelian graph coverings and compare the results with random covers. We discover that the zeta function of the random cover satisfies an approximate Riemann hypothesis while that of the abelian cover does not. See also the authors' article [Contemp. Math. 415, 173189 (2006; Zbl 1222.11109)].